Solutions of the navier-stokes equations and technological applications using matrix distribution with N-methods

IV ABSTRACT SOLUTIONS OF THE NAVTER-STOKES EQUATIONS AND TECHNOLOGICAL APPLICATIONS USING MATRIX-DISTRIBUTION WITH N-METHODS The interaction of an externally imposed magnetic and electric field on the laminar flow of a conducting fluid in a channel is studied using computational techniques. The Navier-Stokes (N-S) equations and the equations describing the electromagnetic field (MHD) are solved simultaneously in a computational fluid dynamics code that utilizes a matrix distribution scheme. The flow considered is two-dimensional on x-y plane. The MHD flow includes an imposed electric and magnetic field acting also on this plane along the central region of the channel and activated by a switch at a specified time (after the vertical flow reaches steady state). A magnet is placed on both sides of the channel and an external magnetic field configuration is obtained in the direction connecting the left and right walls. In addition, an external electric field is applied in perpendicular direction such that ExB becomes opposite to gravitational acceleration direction. This is done to slow down (or even control) the vertical velocity in the channel. The calculations are done with a new solver using a matrix distribution scheme that works on structured and unstructured triangular meshes. The N-S and MHD equations are first written in nondimensional forms and the numerical scheme was obtained. For time iterations, a 3-stage Runga-kutta method is used. The numerical results show that this computer code is capable of resolving different types of problems in different geometries.